1. Field of the Invention
The present invention relates to a fuzzy inference apparatus for conducting a fuzzy inference and to a function generating unit to be employed, for example, in a membership function circuit or a membership function generator of a fuzzy inference apparatus.
2. Description of the Prior Art
A fuzzy inference is achieved in accordance with rules in the form of If . . . then . . . ( modus ponens). The rule is represented in a format "If x is A and Y is B and z is C, then w is D."
In this representation, x, y, and z are input variables of an antecedent, A, B, and C are membership functions thereof, w is a variable of a consequent, and D is a membership function thereof.
In the example above, the antecedent includes three kinds of input variables. In a case of two kinds thereof, the rule is expressed as follows.
"If x is A and y is B, then z is C." Namely, x and y are input variables of an antecedent, A and B are membership functions thereof, z is a variable of a consequent, and C is a membership function thereof in this representation.
The membership functions such as A to D are represented, for example, with linguistic information associated with PL, PM, PS, ZR, NS, NM, NL, etc. In these information items, P, N, L, M, and S denote positive, negative, large, medium, and small, respectively. In consequence, expressions PL and NS stand for positive large and negative small, respectively. ZR indicates almost zero. The linguistic information may be expressed, for example, with binary codes each comprising a plurality of bits.
FIG. 1 shows a conventional fuzzy inference apparatus, which includes a plurality (associated with a number of rules to be established ) of individual inference sections or engines 100 and an integrator section 110 connected thereto. Each inference section 100 comprises membership function circuits ( to be abbreviated as MFC herebelow) 101, 102, and 103 each being supplied with an input variable to produce a signal (e.g. a voltage signal) representing an associated value of a membership of an antecedent, a membership function generator (to be abbreviated as MFG herebelow) 105 for generating a signal representing a membership function of a consequent (e.g. a voltage signal distributed onto 25 lines, which transmit the voltage distribution and which are represented by a hatched bus in FIG. 1; reference is to be made to the U.S. patent application Ser. No. 07/116,777 and the European Patent Application No. 87 116 529.6.), a logic intersection circuit 104 for conducting a MIN operation on outputs from the MFCs 101 to 103, and a logic union circuit 106 for computing a MIN operation on outputs from the logic intersection circuit 104 and the MFG 105. Each of the MFCs 101 to 103 is supplied with a reference voltage (to be abbreviated as R.V. in drawings) corresponding to linguistic information (to be abbreviated as L.I. in drawings), so as to be set to produce a membership function conforming to a rule. Moreover, other parameters of the membership function outputted from the MFC is set by use of a parameter setting unit not shown. The reference voltage defines a peak position (center position ) of the membership function. In this configuration, the MFG 105 is supplied with a code representing linguistic information to produce a membership function associated with the linguistic information. The concluder section 110 includes a logic union circuit 111 for achieving an MAX operation on the membership functions produced from the inference sections 100 and a defuzzifier 112 for defuzzifying an output from the logic union circuit 111 to produce a determinant output. The logic union circuit 111 produces a fuzzy output.
As described above, the conventional fuzzy inference apparatus is provided with an MFC and an MFG for each rule (i.e. for each individual inference section 100). Even a membership function represented with the same linguistic information is required to be set each time the function is assigned to a rule. In consequence, there arise problems that an error occurs in the setting operation and that the setting operation requires a long period of time.
Furthermore, when using such a conventional fuzzy inference apparatus, in a case where two or more inference systems are provided and the membership functions vary between the respective inference systems, it is necessary to prepare the fuzzy inference apparatuses as there are inference systems.
Referring now to FIGS. 2a, 2b and 2c a description will be given of the fuzzy inference process in the individual inference section in a case of two input variables.
The MFCs 101 and 102 are respectively supplied with inputs x.sub.o and y.sub.o such that outputs a and b therefrom are fed to the logical intersection circuit 104. This circuit 104 selects the smaller of the inputs, namely, the output b in this case, so as to output the signal b therefrom. On the other hand, the MFG 105 produces the membership function C. The function C and the output b from the circuit 104 are subjected to an MIN operation in the logic union circuit 106.
As described above, since the MFG 105 outputs a voltage signal which is distributed on a plurality of signal lines to represent a predetermined membership function, the output signal from the MFG 105 is expressed as a set of voltage Ci (i=1 to n) as shown in FIGS. 3a, 3b, In consequence, the results from the MIN operation are also represented as a set of voltage signals distributed on n signal lines and develop values in a discrete form.
Since the MFG 105 outputs a signal distribution on a plurality of signal lines, such plural signal lines are required not only in each inference section 100 but also in the determinant or concluder section 110, which increases the size of the circuit and causes the circuit configuration to be complex. Since the membership function is expressed as a set of signals in a discrete form, there arises also a problem that the shape of the function is restricted by the number of signal lines.
Incidentally, in a fuzzy inference apparatus, a membership function circuit and a membership function generator circuit are necessary as described above. In a case where the membership function circuit or the membership function generator circuit is implemented in a digital circuit, there are in general employed a memory method in which a function value (an output value) is stored in a predetermined location to be accessed by use of a variable value (an input value) as an address thereof or a method in which a form or format of a function formula is registered such that an input value is assigned thereto so as to produce an output value.
However, in the memory method above, in order to improve the precision of the function value to be produced, the interval between variables as addresses is required to be minimized, which leads to a disadvantage that a large memory and a considerable manual operation are necessary for setting the membership function. Moreover, in a case of a membership function representing senses of a human, it is difficult to establish quite complicated items for the senses at the setting phase, and such items do not develop so significant functions.
In the latter case of the method above, since the membership function value is to be computed by a software program, there has been a problem that a long period of time is required.